Downing Street hopes to successfully thrash out with the European Union what a Brexit transition period might look like by the end of the year, according to David Davis.
The Brexit Secretary suggested that agreement over the "form" of the transition could be reached by December.
His comments came after the 27 EU member states agreed in Brussels last week to begin internal discussions on the subject.
Mr Davis told a Commons Exiting the EU Committee that he hoped those talks would progress quickly.
Theresa May has however suggested that no deal on a transition could be struck without agreement over Britain's future relationship with the EU - including on the subject of trade.
The Prime Minister's comments in the Commons led to some business leaders arguing Britain was heading towards a "cliff-edge" Brexit.
But Mr Davis said the Government's aim was to have all negotiations concluded by the time of the UK's withdrawal - set for March 2019.
"What we are intending to do is get the form of the implementation period agreed quickly - December or thereabout. But we want to conclude the overall negotiation by 2019," he said on Wednesday.
"There are a number of reasons for that. One of them is: what is the implementation period taking you towards?
"Are you going from where we are now to a free trade agreement? Are you going from where we are now to what you might call a bare bones agreement, which is WTO (World Trade Organisation) plus agreements on the fundamentals like aviation, and so on? So you need to know where you are going."
Earlier this week, Mrs May said a deal on citizens' rights was "within touching distance".